Prove the trigonometric identity cos(10)^2sec(10)^2=1

 Exercise

$\cos\left(10\right)^2\sec\left(10\right)^2=1$

 

Starting from the left-hand side (LHS) of the identity

$\cos\left(10\right)^2\cdot \sec\left(10\right)^2$

 

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\cos\left(10\right)^2\cdot \frac{1}{\cos\left(10\right)^2}$

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Multiplying the fraction by $\cos\left(10\right)^2$

$\frac{\cos\left(10\right)^2}{\cos\left(10\right)^2}$

 

Simplify the fraction $\frac{\cos\left(10\right)^2}{\cos\left(10\right)^2}$ by $\cos\left(10\right)^2$

$1$

 

Since we have reached the expression of our goal, we have proven the identity

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